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Comment
. 2000 Jul 5;97(14):7678-80.
doi: 10.1073/pnas.150237097.

Taming combinatorial explosion

P Schuster  1
Affiliations
Comment

Taming combinatorial explosion

P Schuster. Proc Natl Acad Sci U S A. .
No abstract available

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Figures

Figure 1
Figure 1
Examples of combinatorial explosion and a catalytic cycle reducing the numbers of possible objects. A shows polynucleotide sequences with increasing chain length n. The number of possibilities is 4n and thus increases exponentially with n. B presents the numbers of possible CmHnOp compounds, computed from simple minded combinatorial expressions assigning three, two, and one possibilities for introducing oxygen containing functions into CH3, CH2, and CH groups, respectively. Clearly, we see an indication of exponential increase. These numbers are compared with those derived in ref. through selection of compounds suitable for a primitive metabolism in early evolution. C presents diagrams for interactions. Here we are dealing with a single class of elements represented by squares. The elements are coupled through their edges to the neighboring squares. We show possible patterns on a two-dimensional (square) lattice. The numbers of these patterns, related to “polyominoes” or “animals” defined in discrete mathematics, increase exponentially with the numbers of squares (2). D, ultimately, represents a cycle of catalytic reactions (3). The catalysts, the enzymes En, are synthesized from substrates Sn. Closure of the cycle leads to an autocatalytic ensemble. Self-enhancement discriminates against molecules that are not members of the cycle and reduces the numbers of possibilities.
See this image and copyright information in PMC

Comment on

  • The origin of intermediary metabolism.
    Morowitz HJ, Kostelnik JD, Yang J, Cody GD. Morowitz HJ, et al. Proc Natl Acad Sci U S A. 2000 Jul 5;97(14):7704-8. doi: 10.1073/pnas.110153997. Proc Natl Acad Sci U S A. 2000. PMID: 10859347 Free PMC article.

References

    1. Morowitz H J, Kostelnik J D, Yang J, Cody G D. Proc Natl Acad Sci USA. 2000;97:7704–7708. - PMC - PubMed
    1. Graham R L, Grötschel M, Lovász L, editors. Handbook of Combinatorics. Cambridge, MA: MIT Press; 1995. pp. 1938–1942.
    1. Eigen M, Schuster P. Naturwissenschaften. 1977;64:541–565. - PubMed
    1. Kauffman S A. J Theor Biol. 1969;22:437–467. - PubMed
    1. Kauffman S A. J Cybernetics. 1971;1:71–96.

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